The diagonal elements in Eq. (REF ) correspond to induced by
perpendicular to graphene plane electric field gap \(U\) . The first term in
Eq. (REF ) gives a pair of parabolic bands \(E=\pm p^{2}/(2m)\) , and the
second term connects with \(\gamma _{3}\)  causes trigonal warping in the band
dispersion. The Lifshitz transition (separation of the Fermi surface) in the
low-energy region occurs at an energy \(\mathcal {E}_{L}=m\mathrm {v}_{3}^{2}/2\simeq 1\)  \(\mathrm {meV}\) , and the two touching parabolas are
transformed into the four separate “pockets” [1]}. The spin and the valley quantum
numbers are conserved. There is no degeneracy upon the valley quantum number
\(\zeta \) . Since there are no intervalley transitions, the valley index \(\zeta \)  one has considered as a parameter.
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